Someone answered this question by saying that black hole entropy conditions and no-hair theorems are asymptotic in nature — the equations give an ideal solution which is approached quickly but never actually reached from the point of view of an observer outside the event horizon.
Since then I've been wondering whether singularities are ever really created, and if not, why do we worry about naked singularities?
Quick recap: to an external observer, an object falling into a black hole experiences time dilation such that it appears to take an infinite amount of time to cross the event horizon and ends up sitting frozen at the border.
So here's my reasoning: the above should also apply during the formation of the black hole in the first place. The gravitational field approaches infinite density as the constituent matter approaches a central point, but to an outside observer, it takes an infinite amount of time for the singularity to form. In other words, it never happens.
As I understand it, naked singularities are dismissed with hand-waving, "we'll fix it when we go quantum," but I don't see that as necessary. It seems to me that singularities never actually form, although event horizons clearly do.
Does this mean that we can stop worrying? What happens in naked singularity scenarios when there is no singularity yet?
Best Answer
Modelling the formation of a realistic black hole can only be done numerically as the process is far too complicated for an analytic solution to exist. However there is a simplified metric for a collapsing non-rotating star called the Oppenheimer-Snyder metric and this captures the basic principles even though it is too simple to be physically realistic.
In the the Oppenheimer-Snyder metric the event horizon appears first at the centre of the star and then grows outwards until it passes the surface, at which point the collapsing star in entirely inside the horizon. The star then completes its collapse into a singularity, and this happens in finite proper time. So if you were on the surface of the star you'd meet your end at the singularity in finite time as recorded by your wrist watch.
It is true that for an external observer the event horizon never forms because it takes an infinite time as measured by the external observer's clock, and so the singularity never forms either. But to use this to claim the singularity never forms is to treat the external observer's time as somehow specially privileged and this goes against the spirit of GR. We should regard all observers are equal, and since the singularity does form in a finite time for the observer falling inwards with the star, it seems reasonable to claim the singularity does form.
It is true that in a universe of a finite age no observer will ever observe an event horizon, or indeed any singularity naked or otherwise, so in this sense we can "stop worrying". What worries physicists is whether the prediction of naked singularities implies some fundamental problem in general relativity. A naked singularity would imply a breakdown of causality and this it seems worrying that a theory which does such a good job of matching experimental observations could predict something that seems at odds with our expectations, even if we could never do an experiment to observe it.
Whether you could form a naked singularity in a finite coordinate time is an interesting question and I don't know the answer. In principle you could start with a rotating black hole, or more precisely an object that is almost but not quite a black hole, and fling mass in to speed up the rotation until it became extremal. However I don't know whether this could be done in a finite time as measured by the external observer.